Мне страшно идти по незнакомой улице ночью.

Russian often expresses physical or emotional states with an impersonal construction:

[person in the dative] + [state word]

So мне страшно literally means something like to me, it is scary, but the natural English meaning is I am scared.

This is the same pattern as:

• Мне холодно = I am cold
• Ему грустно = He is sad
• Нам трудно = It is hard for us

So мне is in the dative case because it marks the person experiencing the feeling.

Here страшно means scary or frightening, but in this pattern it is best understood as I feel scared.

In this sentence, страшно is not the adverb meaning terribly or awfully. It is a state word used as the main predicate of the sentence.

So:

• Мне страшно = I am scared
• not I am scary

If you said я страшный about a man or я страшная about a woman, that would mean I am scary / I look terrible, which is completely different.

After words like страшно, трудно, легко, приятно, Russian often uses an infinitive to show what action feels scary, difficult, easy, pleasant, and so on.

So:

• Мне страшно идти = I am scared to walk / to go
• Мне трудно понять = It is hard for me to understand
• Ей приятно читать = She enjoys reading / It is pleasant for her to read

The infinitive идти tells us what exactly causes the feeling.

This is a very common question with Russian motion verbs.

• идти = to go/walk in one direction, on one occasion, or as a specific action in progress
• ходить = to go/walk habitually, repeatedly, or in general

So Мне страшно идти по незнакомой улице ночью suggests a specific act: walking along an unfamiliar street at night.

If you said Мне страшно ходить по незнакомым улицам ночью, that would sound more general, like:

I’m afraid of walking along unfamiliar streets at night
or
I don’t like doing that in general

With verbs of motion, по often means along, down, around, or through an area.

So идти по улице means:

• to walk along the street
• to walk down the street

It does not mean standing physically on top of the street in the English sense. It is just the normal Russian way to express movement along a street.

Because по here takes the dative case.

The base form is:

• улица = street

After по, it becomes:

• по улице = along the street

And since незнакомой describes улице, the adjective must match the noun in case, number, and gender:

• улица = feminine singular
• dative singular of улица = улице
• dative singular feminine of незнакомая = незнакомой

So:

• по незнакомой улице = along an unfamiliar street

Ночью is the instrumental singular of ночь, and it is often used adverbially to mean at night.

This is very common with parts of the day:

• утром = in the morning
• днём = in the daytime / during the day
• вечером = in the evening
• ночью = at night

So Russian does not need a preposition here.
Ночью by itself already means at night.

Yes, from an English point of view, it may feel like something is missing, but in Russian this is normal.

Russian usually omits the verb быть in the present tense.

So:

• Мне страшно literally looks like To me scary
• but it means I am scared

The present-tense am/is/are is simply not stated.

In the past or future, a form of быть can appear:

• Мне было страшно = I was scared
• Мне будет страшно = I will be scared

Specifically, идти means to go on foot.

In English, translators may sometimes use go if the exact method is not important, but the Russian verb itself refers to movement by walking.

So this sentence most literally suggests:

I’m scared to walk along an unfamiliar street at night.

If the person were going by vehicle, Russian would normally use a different verb, such as ехать.

Yes. Russian word order is more flexible than English word order because the endings show the grammatical relationships.

The original sentence is natural:

Мне страшно идти по незнакомой улице ночью.

But these are also possible:

• Мне страшно ночью идти по незнакомой улице.
• Ночью мне страшно идти по незнакомой улице.
• Мне страшно идти ночью по незнакомой улице.

The basic meaning stays the same, but the emphasis changes slightly:

• putting ночью earlier highlights at night
• putting по незнакомой улице earlier highlights along an unfamiliar street

So word order in Russian often affects focus and style, not just grammar.